cosmjs: Unable to perform `MsgExec` authz transaction in CosmJS

We are building a frontend where the facility of paying gas fee for someone else is being implemented. To do this, we are using the x/authz and x/feegrant module to do the job.

While we could run the /cosmos.authz.v1beta1.MsgGrant and /cosmos.feegrant.v1beta1.MsgGrantAllowance in CosmJS, we were not able to do cosmos.authz.v1beta1.MsgExec transaction, as it gave the error 0uhid is smaller than 100uhid: insufficient funds: insufficient funds.

This is the overall setup of the code for executing MsgExec Tx:

async function execTx() {
  const grantee_mnemonic = " ----- grantee's mnemonic ------"
  const wallet =  await DirectSecp256k1HdWallet.fromMnemonic(grantee_mnemonic, options = { prefix: "hid" })
  
  const client = SigningStargateClient.connectWithSigner(
    "http://localhost:26657",
     wallet,
    { 
        registry: // Custom Module TypeURLs are added ,
        gasPrice: GasPrice.fromString("0.0001uhid"),
    },
  )
  
  let grantee = "hid1k77resf8gktl5wh8fhwlqt7pccandeyj9z5702"  // account with no money
  let customTypeUrl = "/hypersignprotocol.hidnode.ssi.MsgCreateDID"
  
  // The Custom Module Message that the grantee needs to execute
  const txCreateDIDMessage = {
  typeUrl: customTypeUrl,
  value: MsgCreateDID.encode(
      MsgCreateDID.fromPartial({
          didDocString: "---",
          signatures: "---",
          creator: "---",
      })).finish(),
  };
  
  // MsgExec Tx Object
  const txAuthMessage = {
    typeUrl: "/cosmos.authz.v1beta1.MsgExec",
    value: {
        grantee: grantee,
        msgs: [
            txCreateDIDMessage
        ]
    },
  };
  
  const txResult = await client.signAndBroadcast(grantee, [txAuthMessage], "auto");
  return txResult
}

CLI execution (hid-noded tx authz exec tx.json --from <grantee-address> --fee-account <granter's-address> --fees 90uhid) worked fine, but we are struggling with CosmJs execution.